# Antidifferentiation

Antidifferentiation is the process of, given a function \(f(x)\), finding another function \(F(x)\) whose derivative is the given function, \(\frac{d}{dx} F(x) = F^\prime(x) = f(x)\). Antidifferentiation and the antiderivative are part of a larger process called integration. Formally, the antiderivative of \(f(x)\) is the set of functions \(F(x) + C\) such that \[\frac{d}{dx}[F(x) + C] = f(x)\] where \(C\) is what’s called the constant of integration. This can be restated as follows: if two functions \(F(x)\) and \(G(x)\) have the same derivative \(f(x)\), then \(F(x)\) and \(G(x)\) differ by at most a constant \(F(x) = G(x) + C\). …